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The Segal–Bargmann Transform for Lévy Functionals

✍ Scribed by Yuh-Jia Lee; Hsin-Hung Shih

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 292 KB
Volume: 168
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1999.3452

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✦ Synopsis

In this paper, we derive the closed form of the Segal Bargmann transform (or the S-transform) of the Le vy functionals on L 2 (S$, 4) and show that S-transform is a unitary operator from L 2 (S$, 4) onto the space of Bargmann Segal analytic functions on L 2 (R 2 , *), where d*=dt u 2 d; 0 (u) and ; 0 is the Le vy measure.

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